Offers a problem for teachers to try with their students. The problem is presented visually as a row of 15 connected squares and the task is to determine the number of rectangles. The goal is to encourage teachers to reflect on students' work and analyze classroom dialogue. (PVD)

Describes a cooperative learning project with fourth-grade teachers and students. Discusses the K-W-D-L technique (what we know-what we want to know-what we did-what we learned) for mathematical problem solving. Concludes that having students write about their problem-solving experiences connects mathematics and communication skills and enhances…

Describes the Math Pals program which emphasized mathematics communication, allowed students to become active problem solvers with a pal in a different school, and gave students a multicultural experience. (JRH)

Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…

Four surface covering games are presented. These activities are designed to help children learn to develop mathematical theories. Directions for each activity and reproducible game boards are provided. Suggestions for the use of these games are given. (CW)

Presented is a method where a quadratic equation is solved and from its roots the eigenvalues and corresponding eigenvectors are determined immediately. Included are the proposition, the procedure, and comments. (KR)

Discussed is how a separable field extension can play a major role in many treatments of Galois theory. The technique of diagonalizing matrices is used. Included are the introduction, the proofs, theorems, and corollaries. (KR)

Presented are two exercises on the differential geometry of curves. A generalization dealing with smoothness conditions is given that relates the two exercises. Included are the definitions, theorems, propositions, and proofs. (KR)

Presented is a Poisson derivation using explicitly stated assumptions and exact functional equations. The assumptions are homogeneity, independence, and negligibility. Included are the derivations and proofs using L'Hopital's rule for each assumption. (KR)

Explored is an overdetermined system of linear equations to find an appropriate least squares solution. A geometrical interpretation of this solution is given. Included is a least squares point discussion. (KR)

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

Described is the idea of set isometry as examples of Euclidean and non-Euclidean metrics. Included are examples in R squared, preliminaries, and extensions. (KR)

Presented are several models that seem to lead to a better understanding of axiomatics by students. These examples are more like real geometry than the usual examples. Included are the theorems, proofs, and graphs of the functions. (KR)

Two ideas for teaching mathematical Concepts are presented: "Writing Study Cards for Understanding"; and "A Conceptual Approach to Solving Equations." Examples of the applications of these methods are discussed. (CW)

A generalization of the golden ratio is made, called the silver ratio. Some examples where the golden ratio appears are provided so that the silver ratio appears. (MNS)